A tally of points earned by competing athletes during a game or contest. A score can also be a verb: “to keep score” or “to run up the score.” It can refer to a set of data: a “sports score” or a “box score.” The term may also be used figuratively: ”A president’s reelection campaign is all in the box score.”

In recent years, there has been growing interest in quantifying and modeling scoring dynamics in professional sports games. However, relatively little is known about what patterns or principles cut across different sports. By studying a large data set of scoring events from college (American) football, professional hockey, and professional basketball games, we have uncovered several interesting patterns in both the tempo and balance of scoring events.

We find that the timing of scoring events – when they occur during gameplay – is remarkably well-described by a Poisson process, in which each second on the clock produces a scoring event with a sport-specific rate. In contrast, scoring balance – how often one team wins a scoring event – is more closely modelled by a Bernoulli process with a parameter that effectively varies with lead size.

Our results suggest that the underlying dynamic driving this pattern is the impending loss of position at the end of each scoring period, which encourages risky actions in order to maximize chances of success. As a result, the tempo of scoring is depressed at the start and then increases dramatically in the final few seconds of the period.